In the paper we prove that an additive Darboux function
f: **R**-->**R** can be expressed as a
composition of two additive almost continuous (connectivity)
functions if and only if
either f is almost continuous (connectivity) function
or dim(ker(f)) is not equal to 1. We also show that for every cardinal
number K there exists an
additive almost continuous functions with dim(ker(f))=K.
A question whether every Darboux function
f: **R**-->**R** can be expressed as a
composition of two almost continuous functions
remains open.

**LaTeX 2e source file**.
**Requires rae.cls file**
as well as amstex.cls style (class) files.

**
DVI, TEX and Postscript files** are available at the
**Topology Atlas**
preprints side.

**Last modified May 15, 1998.**